Applications of Topological Data Analysis (TDA) for Studying Structural Motifs in Amorphous Bi₂Se₃

Topological materials host unique surface properties that are robust to deformations, thus making them excellent candidates for next-generation computer chips and quantum computing hardware components. In topological crystalline materials, periodicity provides the framework to derive topological invariants. However, in amorphous topological materials, this long range order is not present. In this work, we study the application of topological data analysis (TDA), specifically persistent homology, to amorphous Bi₂Se₃. We show that persistent homology can be used to extract representative structural motifs. We apply persistent homology to an experimentally characterized Bi₂Se₃ slab and MD-simulated Bi₂Se₃ structures compared to reference crystalline Bi₂Se₃ structures to quantify the amount of disorder present. Finally, we determine the relationship between these representative structural motifs and the emergent electronic and topological properties, such as the structural spillage, a topological indicator developed for amorphous systems.